{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Markov chain Monte Carlo\n",
    "\n",
    "The main technical challenge in using Bayesian models resides in calculating the model's joint posterior distribution. \n",
    "\n",
    "Recall that we are interested in combining the information from our data, via the **likelihood** $Pr(y|\\theta)$, and prior information, via the **prior distribution** $Pr(\\theta)$, to produce a joint posterior distribution for the model of interest:\n",
    "\n",
    "$$Pr(\\theta | y) \\propto Pr(y|\\theta) Pr(\\theta)$$\n",
    "\n",
    "However, to guarantee that the posterior is itself a proper probability density (and not just proportional to one), it has to be normalized by dividing by the **marginal likelihood**:\n",
    "\n",
    "$$Pr(\\theta | y) = \\frac{Pr(y|\\theta) Pr(\\theta)}{Pr(y)}$$\n",
    "\n",
    "The marginal likelihood is the numerator, integrated over the parameters $\\theta$:\n",
    "\n",
    "$$Pr(\\theta | y) = \\frac{Pr(y|\\theta) Pr(\\theta)}{\\int_{\\theta} Pr(y|\\theta) Pr(\\theta) d\\theta}$$\n",
    "\n",
    "which, except for very simple (one- or two-parameter) models cannot be calculated analytically.\n",
    "\n",
    "The two alternative strategies to obtaining posteriors for moderate to large models involve either analytic **approximations** or stochastic **sampling**. Approximations are usually valid conditional on assumptions regarding the true posterior distribution, which are typically impossible to validate. Direct sampling strategies rely on our ability to sample from the posterior distribution, and this is frequently not possible. Indirect sampling methods, such as rejection sampling, can be plagued with sampling efficiency issues.\n",
    "\n",
    "The sampling approaches we have introduced so far have each attempted to obtain *independent* samples from the posterior distribution. It turns out, however, that it is possible to generate samples from the posterior distribution using a *dependent* sampling algorithm, and despite the dependence of the samples, one may extract valid inference from them. A class of algorithms called **Markov chain Monte Carlo** yields a Markovian sample (explained below) which, provided that certain conditions are satisfied, is guaranteed to be indistinguishable from a sample drawn from the true posterior itself."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Markov Chains\n",
    "\n",
    "A Markov chain is a special type of **stochastic process**. The standard definition of a stochastic process is an ordered collection of random variables:\n",
    "\n",
    "$$\\{X_t: t \\in T\\}$$\n",
    "\n",
    "where $t$ is frequently (but not necessarily) a time index. If we think of $X_t$ as a state $X$ at time $t$, and invoke the following dependence condition on each state:\n",
    "\n",
    "$$Pr(X_{t+1}=x_{t+1} | X_t=x_t, X_{t-1}=x_{t-1},\\ldots,X_0=x_0) = Pr(X_{t+1}=x_{t+1} | X_t=x_t)$$\n",
    "\n",
    "then the stochastic process is known as a **Markov chain**. This conditioning specifies that the future depends on the current state, but not past states. Thus, the Markov chain wanders about the state space, remembering only where it has just been in the last time step. The collection of transition probabilities is sometimes called a **transition matrix** when dealing with discrete states, or more generally, a\n",
    "**kernel**.\n",
    "\n",
    "In the context of Markov chain Monte Carlo, it is useful to think of the Markovian property as “mild non-independence”. MCMC allows us to indirectly generate independent samples from a particular posterior distribution.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Why MCMC Works: Reversible Markov Chains\n",
    "\n",
    "Markov chain Monte Carlo simulates a Markov chain for which some function of interest\n",
    "(*e.g.* the joint distribution of the parameters of some model) is the unique, invariant limiting distribution. An invariant distribution with respect to some Markov chain with transition kernel $Pr(y \\mid x)$ implies that:\n",
    "\n",
    "$$\\int_x Pr(y \\mid x) \\pi(x) dx = \\pi(y).$$\n",
    "\n",
    "Invariance is guaranteed for any **reversible** Markov chain. Consider a Markov chain in reverse sequence:\n",
    "$\\{\\theta^{(n)},\\theta^{(n-1)},...,\\theta^{(0)}\\}$. This sequence is still Markovian, because:\n",
    "\n",
    "$$Pr(\\theta^{(k)}=y \\mid \\theta^{(k+1)}=x,\\theta^{(k+2)}=x_1,\\ldots ) = Pr(\\theta^{(k)}=y \\mid \\theta^{(k+1)})=x$$\n",
    "\n",
    "Forward and reverse transition probabilities may be related through Bayes theorem:\n",
    "\n",
    "$$Pr(\\theta^{(k)}=y \\mid \\theta^{(k+1)}=x) = \\frac{Pr(\\theta^{(k+1)}=x \\mid \\theta^{(k)}=y) \\pi^{(k)}(y)}{\\pi^{(k+1)}(x)}$$\n",
    "\n",
    "Though not homogeneous in general, $\\pi$ becomes homogeneous if:\n",
    "\n",
    "-   $n \\rightarrow \\infty$\n",
    "\n",
    "-   $\\pi^{(i)}=\\pi$ for some $i < k$\n",
    "\n",
    "If this chain is homogeneous it is called reversible, because it satisfies the **detailed balance equation**:\n",
    "\n",
    "$$\\pi(x)Pr(y \\mid x) = \\pi(y) Pr(x \\mid y)$$\n",
    "\n",
    "Reversibility is important because it has the effect of balancing movement through the entire state space. When a Markov chain is reversible, $\\pi$ is the unique, invariant, stationary distribution of that chain. Hence, if $\\pi$ is of interest, we need only find the reversible Markov chain for which $\\pi$ is the limiting distribution.\n",
    "This is what MCMC does!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Metropolis-Hastings Algorithm\n",
    "\n",
    "One of the simplest and most flexible algorithms for generating reversible Markov chains is the Metropolis-Hastings algorithm. Since we cannot sample directly from the (unknown) posterior distribution, this algorithm employs an **auxilliary distribution** that is easy to sample from. These samples generate candidate state transitions, which are accepted or rejected probabilistically.\n",
    "\n",
    "![](images/Metropolis.png)\n",
    "\n",
    "Let us first consider a simple Metropolis-Hastings algorithm for a single parameter, $\\theta$. We will use a well-known statistical distribution to produce candidate variables $q_t(\\theta^{\\prime} | \\theta)$. Each generated value, $\\theta^{\\prime}$, is a *possible* next value for\n",
    "$\\theta$ at step $t+1$. \n",
    "\n",
    "Whether or not $\\theta^{\\prime}$ is accepted depends on the relative probability of the new value versus the current value, weighted by the probabilities of the two values under the proposal distribution: \n",
    "\n",
    "$$a(\\theta^{\\prime},\\theta) = \\frac{q_t(\\theta^{\\prime} | \\theta) \\pi(\\theta^{\\prime})}{q_t(\\theta | \\theta^{\\prime}) \\pi(\\theta)}$$\n",
    "\n",
    "This is the **acceptance ratio**, and is used as a threshold value for a uniform random draw that determines acceptance:\n",
    "\n",
    "$$\n",
    "\\theta^{(t+1)} = \n",
    "\\begin{cases}\n",
    "\\theta^{\\prime}  & \\text{with prob. } p = \\min(a(\\theta^{\\prime},\\theta^{(t)}),1)\\cr\n",
    "\\theta^{(t)}  & \\text{with prob } 1 - p\n",
    "\\end{cases}\n",
    "$$\n",
    "\n",
    "This transition kernel implies that movement is not guaranteed at every step. It only occurs if the suggested transition is likely based on the acceptance ratio.\n",
    "\n",
    "A single iteration of the Metropolis-Hastings algorithm proceeds as follows:\n",
    "\n",
    "1.  Sample $\\theta^{\\prime}$ from $q(\\theta^{\\prime} | \\theta^{(t)})$.\n",
    "\n",
    "2.  Generate a Uniform[0,1] random variate $u$.\n",
    "\n",
    "3.  If $a(\\theta^{\\prime},\\theta) > u$ then\n",
    "    $\\theta^{(t+1)} = \\theta^{\\prime}$, otherwise\n",
    "    $\\theta^{(t+1)} = \\theta^{(t)}$.\n",
    "    \n",
    "\n",
    "### Random-walk Metropolis-Hastings\n",
    "\n",
    "We still have not talked about how to choose the proposal $q$. In principle, it can be just about anything, but some choices are wiser than others. A practical implementation of the Metropolis-Hastings algorithm makes use of a **random-walk** proposal.\n",
    "\n",
    "A random walk is a Markov chain that evolves according to:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\theta^{(t+1)} &= \\theta^{(t)} + \\epsilon_t \\\\\n",
    "\\epsilon_t &\\sim f(\\phi)\n",
    "\\end{aligned}$$\n",
    "\n",
    "As applied to the MCMC sampling, the random walk is used as a proposal distribution, whereby dependent proposals are generated according to:\n",
    "\n",
    "$$q(\\theta^{\\prime} | \\theta^{(t)}) = f(\\theta^{\\prime} - \\theta^{(t)}) = \\theta^{(t)} + \\epsilon_t$$\n",
    "\n",
    "Generally, the density generating $\\epsilon_t$ is **symmetric** about zero,\n",
    "resulting in a symmetric chain. Chain symmetry implies that\n",
    "$q(\\theta^{\\prime} | \\theta^{(t)}) = q(\\theta^{(t)} | \\theta^{\\prime})$,\n",
    "which reduces the Metropolis-Hastings acceptance ratio to:\n",
    "\n",
    "$$a(\\theta^{\\prime},\\theta) = \\frac{\\pi(\\theta^{\\prime})}{\\pi(\\theta)}$$\n",
    "\n",
    "The choice of the random walk distribution for $\\epsilon_t$ is frequently a normal or Student’s $t$ density, but it may be any distribution that generates an irreducible proposal chain.\n",
    "\n",
    "An important consideration is the specification of the **scale parameter** for the random walk error distribution. Large values produce random walk steps that are highly exploratory, but tend to produce proposal values in the tails of the target distribution, potentially resulting in very small acceptance rates. Conversely, small values tend to be accepted more frequently, since they tend to produce proposals close to the current parameter value, but may result in chains that mix very slowly.\n",
    "\n",
    "Some simulation studies suggest optimal acceptance rates in the range of **20-50%**. It is often worthwhile to optimize the proposal variance by iteratively adjusting its value, according to observed acceptance rates early in the MCMC simulation ."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Linear model estimation\n",
    "\n",
    "This very simple dataset is a selection of real estate prices, with the associated age of each house. We wish to estimate a simple linear relationship between the two variables, using the Metropolis-Hastings algorithm.\n",
    "\n",
    "$$\\mu_i = \\beta_0 + \\beta_1 a_i$$\n",
    "\n",
    "$$p_i \\sim N(\\mu_i, \\tau)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "age = np.array([13, 14, 14,12, 9, 15, 10, 14, 9, 14, 13, 12, 9, 10, 15, 11, \n",
    "                15, 11, 7, 13, 13, 10, 9, 6, 11, 15, 13, 10, 9, 9, 15, 14, \n",
    "                14, 10, 14, 11, 13, 14, 10])\n",
    "price = np.array([2950, 2300, 3900, 2800, 5000, 2999, 3950, 2995, 4500, 2800, \n",
    "                  1990, 3500, 5100, 3900, 2900, 4950, 2000, 3400, 8999, 4000, \n",
    "                  2950, 3250, 3950, 4600, 4500, 1600, 3900, 4200, 6500, 3500, \n",
    "                  2999, 2600, 3250, 2500, 2400, 3990, 4600, 450,4700])/1000."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(age, price)\n",
    "plt.xlabel('Age')\n",
    "plt.ylabel('Price');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function calculates the joint log-posterior, conditional on values for each paramter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import gamma, norm\n",
    "dgamma = gamma.logpdf\n",
    "dnorm = norm.logpdf\n",
    "\n",
    "def calc_posterior(a, b, t, y=price, x=age):\n",
    "    # Calculate joint posterior, given values for a, b and t\n",
    "\n",
    "    # Priors on a,b\n",
    "    logp = dnorm(a, 0, 10000) + dnorm(b, 0, 10000)\n",
    "    # Prior on t\n",
    "    logp += dgamma(t, 0.001, 0.001)\n",
    "    # Calculate mu\n",
    "    mu = a + b*x\n",
    "    # Data likelihood\n",
    "    logp += sum(dnorm(y, mu, t**-0.5))\n",
    "    \n",
    "    return logp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "rnorm = np.random.normal\n",
    "runif = np.random.rand\n",
    "np.random.seed(42)\n",
    "\n",
    "def metropolis(n_iterations, initial_values, prop_var=1):\n",
    "\n",
    "    n_params = len(initial_values)\n",
    "            \n",
    "    # Initial proposal standard deviations\n",
    "    prop_sd = [prop_var]*n_params\n",
    "    \n",
    "    # Initialize trace for parameters\n",
    "    trace = np.empty((n_iterations+1, n_params))\n",
    "    \n",
    "    # Set initial values\n",
    "    trace[0] = initial_values\n",
    "        \n",
    "    # Calculate joint posterior for initial values\n",
    "    current_log_prob = calc_posterior(*trace[0])\n",
    "    \n",
    "    # Initialize acceptance counts\n",
    "    accepted = [0]*n_params\n",
    "    \n",
    "    for i in range(n_iterations):\n",
    "    \n",
    "        if not i%1000: print('Iteration %i' % i)\n",
    "    \n",
    "        # Grab current parameter values\n",
    "        current_params = trace[i]\n",
    "    \n",
    "        for j in range(n_params):\n",
    "    \n",
    "            # Get current value for parameter j\n",
    "            p = trace[i].copy()\n",
    "    \n",
    "            # Propose new value\n",
    "            if j==2:\n",
    "                # Ensure tau is positive\n",
    "                theta = np.exp(rnorm(np.log(current_params[j]), prop_sd[j]))\n",
    "            else:\n",
    "                theta = rnorm(current_params[j], prop_sd[j])\n",
    "            \n",
    "            # Insert new value \n",
    "            p[j] = theta\n",
    "    \n",
    "            # Calculate log posterior with proposed value\n",
    "            proposed_log_prob = calc_posterior(*p)\n",
    "    \n",
    "            # Log-acceptance rate\n",
    "            alpha = proposed_log_prob - current_log_prob\n",
    "    \n",
    "            # Sample a uniform random variate\n",
    "            u = runif()\n",
    "    \n",
    "            # Test proposed value\n",
    "            if np.log(u) < alpha:\n",
    "                # Accept\n",
    "                trace[i+1,j] = theta\n",
    "                current_log_prob = proposed_log_prob\n",
    "                accepted[j] += 1\n",
    "            else:\n",
    "                # Reject\n",
    "                trace[i+1,j] = trace[i,j]\n",
    "                \n",
    "    return trace, accepted"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's run the MH algorithm with a very small proposal variance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 0\n",
      "Iteration 1000\n",
      "Iteration 2000\n",
      "Iteration 3000\n",
      "Iteration 4000\n"
     ]
    }
   ],
   "source": [
    "n_iter = 5000\n",
    "trace, acc = metropolis(n_iter, (1,0,1), 0.001)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the acceptance rate is way too high:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.9664, 0.9522, 0.9486])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(acc, float)/n_iter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for param, samples in zip(['intercept', 'slope', 'precision'], trace.T):\n",
    "    fig, axes = plt.subplots(1, 2, figsize=(8, 2))\n",
    "    axes[0].plot(samples)\n",
    "    axes[0].set_ylabel(param)\n",
    "    axes[1].hist(samples[int(n_iter/2):])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, with a very large proposal variance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 0\n",
      "Iteration 1000\n",
      "Iteration 2000\n",
      "Iteration 3000\n",
      "Iteration 4000\n"
     ]
    }
   ],
   "source": [
    "trace_hivar, acc = metropolis(n_iter, (1,0,1), 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.0152, 0.0008, 0.0172])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(acc, float)/n_iter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for param, samples in zip(['intercept', 'slope', 'precision'], trace_hivar.T):\n",
    "    fig, axes = plt.subplots(1, 2, figsize=(8, 2))\n",
    "    axes[0].plot(samples)\n",
    "    axes[0].set_ylabel(param)\n",
    "    axes[1].hist(samples[int(n_iter/2):])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to avoid having to set the proposal variance by trial-and-error, we can add some tuning logic to the algorithm. \n",
    "\n",
    "## Auto-tuning Metropolis-Hastings\n",
    "\n",
    "We can modify the Metropolis-Hastings algorithm above by adding logic to automatically change the proposal scale depending on the acceptance rate of the chain. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def metropolis_tuned(n_iterations, initial_values, prop_var=1, \n",
    "                     tune_for=None, tune_interval=100):\n",
    "     \n",
    "    n_params = len(initial_values)\n",
    "             \n",
    "    # Initial proposal standard deviations\n",
    "    prop_sd = [prop_var] * n_params\n",
    "     \n",
    "    # Initialize trace for parameters\n",
    "    trace = np.empty((n_iterations+1, n_params))\n",
    "     \n",
    "    # Set initial values\n",
    "    trace[0] = initial_values\n",
    "    # Initialize acceptance counts\n",
    "    accepted = [0]*n_params\n",
    "     \n",
    "    # Calculate joint posterior for initial values\n",
    "    current_log_prob = calc_posterior(*trace[0])\n",
    "     \n",
    "    if tune_for is None:\n",
    "        tune_for = n_iterations/2\n",
    "     \n",
    "    for i in range(n_iterations):\n",
    "     \n",
    "        if not i%1000: print('Iteration %i' % i)\n",
    "     \n",
    "        # Grab current parameter values\n",
    "        current_params = trace[i]\n",
    "     \n",
    "        for j in range(n_params):\n",
    "     \n",
    "            # Get current value for parameter j\n",
    "            p = trace[i].copy()\n",
    "     \n",
    "            # Propose new value\n",
    "            if j==2:\n",
    "                # Ensure tau is positive\n",
    "                theta = np.exp(rnorm(np.log(current_params[j]), prop_sd[j]))\n",
    "            else:\n",
    "                theta = rnorm(current_params[j], prop_sd[j])\n",
    "             \n",
    "            # Insert new value \n",
    "            p[j] = theta\n",
    "     \n",
    "            # Calculate log posterior with proposed value\n",
    "            proposed_log_prob = calc_posterior(*p)\n",
    "     \n",
    "            # Log-acceptance rate\n",
    "            alpha = proposed_log_prob - current_log_prob\n",
    "     \n",
    "            # Sample a uniform random variate\n",
    "            u = runif()\n",
    "     \n",
    "            # Test proposed value\n",
    "            if np.log(u) < alpha:\n",
    "                # Accept\n",
    "                trace[i+1,j] = theta\n",
    "                current_log_prob = proposed_log_prob\n",
    "                accepted[j] += 1\n",
    "            else:\n",
    "                # Reject\n",
    "                trace[i+1,j] = trace[i,j]\n",
    "                 \n",
    "            # Tune every 100 iterations\n",
    "            if (not (i+1) % tune_interval) and (i < tune_for):\n",
    "         \n",
    "                # Calculate aceptance rate\n",
    "                acceptance_rate = (1.*accepted[j])/tune_interval\n",
    "                if acceptance_rate<0.2:\n",
    "                    prop_sd[j] *= 0.9\n",
    "                elif acceptance_rate>0.4:\n",
    "                    prop_sd[j] *= 1.1\n",
    "                accepted[j] = 0\n",
    "                 \n",
    "    return trace[tune_for:], accepted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 0\n",
      "Iteration 1000\n",
      "Iteration 2000\n",
      "Iteration 3000\n",
      "Iteration 4000\n",
      "Iteration 5000\n",
      "Iteration 6000\n",
      "Iteration 7000\n",
      "Iteration 8000\n",
      "Iteration 9000\n"
     ]
    }
   ],
   "source": [
    "trace_tuned, acc = metropolis_tuned(10000, (10,0,1), tune_for=5000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.2702, 0.2922, 0.2932])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(acc, float)/5000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for param, samples in zip(['intercept', 'slope', 'precision'], trace_tuned.T):\n",
    "    fig, axes = plt.subplots(1, 2, figsize=(8, 2))\n",
    "    axes[0].plot(samples)\n",
    "    axes[0].set_ylabel(param)\n",
    "    axes[1].hist(samples[int(len(samples)/2):])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A useful way to informally examine the fit of the model is to examine functions of the posterior distribution. For example, here are 50 random regression lines drawn from the posterior:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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OZJLHVVZyDN3dND/z+Sj2mQx/L/SvGRkBfvAD4EtfYiXO+DjHGotx0tq3j+eSqL6iwqWUpNyysLWgpKvGxzm5ANpcXFG2MGsV+GMAbgXwrwDea619yBhz1Fp7yzWOOwTgEQAvstY+aox5D4AZa+2fLHndYQCHAaC9vf2Onivtc78Wp045a4BAgBHq2BidJI8dY036yAjz5QAFraGBi6I7dlAoOzsphBLdp9OLNy5NTlLYp6ZcpU5hXXpFBQVSxhAO832k7HFykseKh00q5a4IurtpgNbSwqhbavClTLKqip+pr48Nxr/4RX7mmRlOLFVVFPqDB2mTUF/vOksVppmqqxcLuPSblQlIm4srypZjrQL/FjBqPwrgpwC0A/i4tfbF1ziuEcAj1trO/P0XA/if1tqfWu6YVW90+tznnPVALEbxbmykqHk8fO7UKTYFOXnSLbRmMjymupr58fZ2F90XVqmkUqy+efZZpnHEeyYe58TR27u4Bl4ieVnYlBaAkQjTIePjrmZ/bs7teK2r43vv3+92zRa6UtbVOVfK06eBL38ZePBBvr9cHTQ2Uuz37eMVS10dJx/ZhFVV5XbMFiLloJOT7kpCm4sryqanqBudjDEGgNdam7mO134HwG9Za0/lyy7D1tr/d7nXr7qKRvzgh4d5m5114lhbS8FvanJ5aRHrwp6t8biroJGdrxLdt7e7RclEgiJ/4gQnipkZin0mw3LMixcp+mJhUFZGgRVhlUhfrIwnJ10J58wMJyxZP9i3j+8v1S/SalC6ShnDYx97DPjCF1iNMzrqjM9aWhjVd3Xxs0gJaDbLcUmDkqWL0JKvlx24gYATe83XK8qmYrVlkr+e/zVurf3UKt/4VrBMsgzAeQC/aa2dXO71a8rBC9ZyUVT820dGXGPsQIAiJQ09wmEK87PPMhVz6hSPEWEToW1tddH9rl0UO4+HQnjuHG9SH28tBba/nxOB1ODLhiVpEtLYSLEWsc9mOSmIgdnsrNup2tzMRdX2dmevIH1hJVefy3EM3/oWUzhPP81zSDllWxvFvrOTn6Gy0u3QjUbdjtnCtEw2+9zm4lLiqc3FFWVTsFqB/9P8r3PW2r9er8EVUhSBvxJzcxTaoaHF5l3SqKO+3i2MjoxQ7E+eZOpDqmH8fifMbW2uFLOtjSJ86RLLHPv7GYknkxTQRIKTzenTfI1cXQAU9qoqTjhS4x4IMAWTSnGikjROLsfnGhoo9k1NnCAkoi8U6GSS+fovfAH45jc5ASUSbgFX0lDd3fwcodDitIz42hci+XptLq4om4rS9qJZKZkMBXhkhMI7N+dy5+EwI9RolL8nk0y5nD7NaHxszC3UhkKcGFpaGOF3d1Pwg0Gmbs6f52QinaQKrQWkpHNmxj0nC65ydSGVOYUTxcwM31/SOI2NFOiGBlcx09Tkonrxmn/mGeD++2mTMDzsSj7r6nj8zp2ss+/q4me72sIssLi5uEwM2lxcUTaE1UbwPgBvAPAaAC3gTtRBAJ8H8CFrbbrYA70hAl+INP2Ynnadm2Sjks9HkQyFKP5eLycF6d8qfjPpNF8nkXhLi8vdRyIU1N5e1+ovk3GNRMbGmBaSXH4i4Rp0V1dT6GWDldfLY2XReGaGY0+nOSnV13OikfWGlha37iDvOzLCKpyvftXtmpUa/IYGpm+kdLO52W3YKrQyXvr9zcy4fH3h2AvdMBVFWTdWK/CfADAF4KMA+vMPtwJ4HYBqa+0vFnugN1zgl5JMuuqW2VmXKvF63c3jcRuHenp4k4VdSf1I2qS5maLb1cUJQER9ft5ZIIhfjaR4+vqcI6YsFC8VexFej4fjk/dOJhlB19byvdvaXDpJulQBPHdPD3P1Dz/MtJKkcCIRTgzNzYzq9+3j+4t4y8LsUu+fbNY1F5erHLFtKMHm4oqyWVitwJ+y1u5Z5rnT1trdRRwjgE0g8IXkchT76Wne0mkKrtdLcROhF8fJixddw25xsTSGQi65++ZmCm1VFc+3sOBKJAHnVyMpnt5eV2UjDpYSTUueXCYBn49jWVig2CcSbrdqczNr/iXvXlXlOllNTzN186Uv0dZYDNiCQdeCsKWFdfo7d7qdwLEYx3Cl/PtyzcXFOE3z9YpSNFYr8I8A+GsAn7HW5vKPeQD8ZwC/b619frEHuqkEfikLC07sZQeo388o1eej8MfjfH5gwC3SSjSezVKgZVG3ro5CW1hFIz7y2awrnezr4yJpX5+L/mXBNRJZbDcgpZR+vzuHRPbiG9/ayhTSwYMUfInqUymuCzzwANM44oUjJZdii9Dezjr99nZ+dqnRF2O2K31vJdhcXFE2C6sV+E4A/z+AlwGYBGAAVAL4Jrhh6UKxB7qpBb6QTMaJvdSuS2pGdq5mMhTjvj6WYZ47RwGVjU0+n8udi5eNVKWEwxRkr5fiLDn3nh6ep7eXawCSCikr4/FVVTyn3+8ekwkjHud4xLqhpoaR+f79FPtdu1xkPTvLOv8vfYk19qOjrjm5iH1VFUX+wAG3KCylm1cqoSyx5uKKsllYcxWNMaYm/9qxYg+ukC0j8IVIlyURfGn5Fwi4ZtuBgNv1evIk8OSTzthsfp7CWlZGYRSxl41Rra2uIkZsiefnefzZsxT9kRFnWiYeORUVvDLw+Vy3KqmXTyYptpJ3b2hgrv6mm+hl39LCz5DN8qrh4Ye5Y/bUKec3Lykc8acXIzXZhCXllleK0qWiSHb0AluuubiibBbW0tFpL4CfxZIqGmvtyfUY6JYU+KUkkxR6qV+XvH0sxls0SgGLx1l++cQT3FE7OOiMzLxe52cTDjvrBVmsTSTcImwyyaj+7Fnm7aWUU9I9FRUUdrkiEJvjigqmTFIpt8ZQVube5+abXXRuDMd78SLwla9wx+zQkOtXGwzyvJLzb21lzr+x0dXoX2lhFnDNxScm3LqF2DxosxJFuSarTdH8IYBfBvBvWFxF80sA/s1a+5fFHmhJCHwh0kZwaorinc5XlkqaIxZzG4omJrjI+dhjFOrRUbfBSSJ8qZARR8y6Ogq02CKkUhThU6d4jpERiqaIvawXGOMagVRWUpyzWVdFlE7ztY2NTN1ICqeuzu3g/eEPWW759NM8RnbphsP8TJLzb2qi4Mt+geUWZgHXXFyalWhzcUW5JqsV+NMADiytd8837jhmre0u9kBLTuCXIjX3UmUDUAhF7KUTVSrFqPzJJ5m/HxpyVwTptNuUVVXF1MiuXayUkRp5OUdvL+vdpbonlaKwlpe7xVWPx5mQiZDmchyrLOhGIhToPXt4k0bhxvDK4+tf58KsmJ5JC0SZUAobkkh039Gx/MIssDhfL9452lxcUZ7DagX+JICfsNb2LHm8A8ADy5VQroWSF/hC0unFC7W5nOsCJYJfVsbHh4cp1OJmKS35JCcvu2Dr6yn4YhcsG7QWFijEx4/zeFk09XhciWUux5s0JxGvHsClcCSilnx7ezt/r6nhsU8/zSqcxx9nqsgYXq2IKMtegsJF2t27eUUi/j5LkVJOyddrc3FFWcRqBf6VAN4L4AyAvvzD7QB2Afgda+1Xiz3QbSXwhUiFiQh+MsnHZXE0FqPYGkORO32aefuzZ53lglgY+P3uakBEUMS6ooJpkKEh1xRlfNzZDfj9HIvstvX73S7XUMiNE+Bz9fW8cti1yy3UVlbySuN732Nkf+YMJxhZRK6rW5wmCod5jJRudnQsXz4pzcVlcgO0ubiy7VnLIqsHwJ3gIqsBc/E/tNZm12Og21bgl5JIOLGXhVqfj2Imgi/WBT09rotVX59rbCILoFI2GQ5TpCVVEosxZTM6ygmjr4+bqqR8UdI8qRQfKyzrLNwRK4usYo/Q3o6vPVaN//WhVpwZDOG2hkH82cu+gTvTj3BsqZQ7j4i9+PH4/Xxszx4u8ra3Lx+hJxKuWYk2F1e2MWsReAMn8FJF84Pr7bG6UlTgr0A2u3hHbSbjUh8i9pLHHh1l/fozz7AcUyyMAQppOMyJQczNCqP8VIqvHxhghD897Y7zehkxp1J8/7IyThbSvcoYPhcO48SlGD7xUAsGsvW4hCZMogoz5Q24988tfnbvKeChh3j1MTXlUj4tLZx4AAp3Ou3KNw8eBG69lVcKy4n2cs3Fq6u1WYlS8qw2RfPjAP4BTNEM5B9uBVM0b7bWPlDsgarAX4NCc7TpaVc9I52sJDVjDKPrs2dZhnn0qKuVlxJM8cKR9IyYhElkPzHBhVmxG5B8vjE8j+zOlTr7/Kaqr3zdg7mkB9OoxDhqcQmNmEAtUFuHj34u39JweppjeuQRLszG4zxHQwMXYcWrfm6O71VWxkngtttYpy+TwVK0ubiyDVmtwJ8A8Cpr7cUlj3cB+D/W2n3FHqgK/AqRGvbpadcgRLpSieD7/S6V8+ijFNZLl9yGrFDICXcy6URRziEbtEZHnXeO7JRNpynCCwuXG31/52g5kgggDT8y8CGOEEZRixE04B1/3+DKHmVsfX2chI4f53tY6wzPpO5fmqDMzHBi6uwEbr+dkf3V8vWTkxR7uYrR5uJKCbJagT8DYN/S1nz5Msnj1tpdxR6oCvwayOUWL9SmUnw8FFq8UAtQ7B9/nKmcvj5npBYIMCrPZnk/nXZmaRUVFPKxMQp+IuHKF2USmZvDU4/EkbUZ5GCQRjmyMMigHFlPEK94bcyZrklZpuzcnZ3lguzTT7Osc2HB+dZ0dTEfH4tRsIeHGdmHQlzgveMOpnKWK5/c4ObiR44A99zDi5X2duDee4G7717Xt1S2EasV+LcB+C/gRiepomkDNzp90lr7zmIPVAW+iIjxmSzUAkynFO6oBVg++dRTzN3397sKHmMo4KkUhV7EXPxuZIF2dNT52Pv9+No3PbC5NIKII4AUDLIALHwwuP02j1vwlVaIjY0UW2kO7vdzHeDYMS7+jo1dzu+jtpZllTt28LNcusQJKpnk5+nuBp7/fIr+cvX1yzUXFw+gInPkCHD4sNv2AHBeuu8+FXmlOKxlkXUfnFWBVNF8wVp7fD0GqgK/TkgXKxF8MUeThdrKSj4mXjnnz7uOU7KAmslQSMVhEnAbo6y97C3zlc/HYZGFhQc+ZOFFBiHE4UUWz781n/O31m24ikQo8h0drnVhbS1VUNYRjh1j+Cu9baNRTg579lDMMxlG/b29HGtNDZ+7/XZOBlcS+xvUXLyzkxdMS+no4JAVZa1oyz7FUbhQOzXlcvHiNR+JMGKXJiRSejk56Zwt02n+lI5S1l6us//Ax8uQjKdQiWmUIwkvMvAji6g/jZc+P+k8dOQ42XAlVsrNzcxjNDdTaOvqGNWPjHD94Px5pmikk1ZlJW0bDhyg6M/N8WpkeJiTVm0tHTNvuompnit1mVrH5uIej2vBW4jY8SvKWim6wBtjvmKtfdWaR7YEFfgNQMzRZKFWzNGiUbeQKhU7Y2MuBz456Xxw4vHLvW37+nJ44qgX06hAHOXIwouQyeDFz09hZ0s+3SPHyOKsXB1ks87TprKSIt/czDC4vp5inUxS5J9+mhH79LS7GqmvZwrn1lspziMjjP5HRviaujqK/f79POeVxD6VcjuFi9BcXCN4Zb1ZbQ7+9uXOB+BL1tqmIo3vMirwG8yVulgBbvEynXYpFnGBHBpi7l68axYWcO7YAs4+s4BMMoVQuUHXvnJ0dgcYiQcCbhOViPz8PH/PZPi4WDAU7nSVfrOy4FpZyTE+8wwrcAYHKf4+H5/r6GC7wVtu4TnOnnU5fZ+PYr9vH9sSdnZeOSWzsODEvrC5eHX1dTcr0Ry8st6sVuCzAB4CBX0pd1lri+74pAK/ybhSFytrKb6SIpHb5KRrWyhdrGZnXc28ROvityNWxsGg6zqVSvFKQHL9cg5J44TDjKKlwfiuXbyVl3OieeopCvnYGJDNYnA6hCd6anE02Y3+6tvwU2/txqt/0jKFc/48xym7Z6XZeEfHc8V+jc3FtYpGWU9WK/DPAvg5a+2ZKzzXZ61tK+4wVeA3NUu7WEnHKsmlSzenykqK4OnTzrJY3DOlIcrsrDMvKy/nsdEobyLw4nVfKPTily+9bqULVns7Bfqmmziu3l6c/vRT6PlOD0KYBWCxgAoMmnYc/C/7ccdv3UHfnJkZLir39Heari8AACAASURBVPD8fj8/w44dTON0dGhzcWXTs1qB/wUAz1hrT13huddYaz9X3GGuTuA1OtoAlnaxkvr7hQUKdlUVI+y6Otf+T1oNyoYl2SA1M0PR93qd347c4nFXz5/LufSNTDJS0un1ug5Tra1AdzcOv/cgJmdy2IWzuAnH0YghBLEAn8+L572skpH/bbdxUqip4YLy+fMu3eT383Ps3Oki+6XifbXm4rGYmp8tg/7NFpeSraLR/OYmobCLlXjXLyy4blSdnRT7ZJKR/enTTOWMjLidppLOicfdzlqxTg6FGDmLKZnk8CWyzy/wIpe7XO74vWcDGEM9zqMTp7ELBkAr+rAXZ/Fzd426vrhNTRTwu+6i6Pv9/Aw9PRR9sXeIxSj20nB8qdjH4y5fr83Fl0X/ZovPmtwkrbW5gvt3A4gA+Bdr7cKyB66SlQq8VihsQrJZfPJDs3jfO0bhG+zF3tox/MovpPGin6hgWqSrixFuLscQ7uRJ7mDt73cdqORqQKpYJJUjfWWl9tAYt+CbTLp8fyKBZ5/NwOayyMCLFMowiVoMoR6zFa14y381FHGZjMRTv62Ni7J33UURn5vj2oI0OZf+uZEIJ4P9+3lModiLpfLExGV3zi8/WIZ3vLcGzwxUo6EjsK0jVv2bLT5rEfivAPh9a+0JY8w9AF4C4DyAFmvtzxR7oCsVeK0x3nwsjdBCmMfOwAD+5r/14BU3jfAfLBqlgEo1jMdDQTx5ktH92bMsxRwbo6jKBqdMxjUNkV2vfr97LJt3sU6l0H92HqeOpVGGOMqQgg9ZeGDR2u5HXVfU7V7NZp2NgUTr0Sjz8Hfeyc1SVVWuo9bQEMVevH9iMb72wAGKfWHNfC6HT31gCn/2e+PwJ9hcfAEhxIM1+It/rMav/Pr2y9fr32zxWW0O/qUAPgTg9WAlzT8B+CMA4wA+AOC3AFy01vYWa6AawW99rvpvciLfuFsajQCuQ1RTk+tilUpR6I8fdxYKw8MuFVOoEhLhl5U5G+P88+cvWJx4JoN0Mo2IP419OxNojsSdx730qa2o4E/ZkSubunw+7rLdu5dR/cGDPLeUhI6P86pjaoqTT2EaJy/28n34kEY1JlCNCYSwgMZGgy9/Z/s1F9e/2eJzNYG/VgjhARAFEAaQBTAGin1Czl2sQa6Ge++9cj7v3ns3bkzbnd5lpvveXjANsm8fb3Nz/Ivu66OInzpFoWtspOh1djIqtpYCf+wYa97PnmXNu1TySPSeSDgztHy9/Y7WCHZ0+gDrBUwQQJTCns3ytZL7n56mmAcCFPqWFp57dpYRe28v8PDDHNtNNzGy37+fgt7ezveenOQk9NRTdMfMi32u5wAMWpGBHyNowAgaEEAcw5cmgPgEWygWNhevqCjpZiX6N3tjuVaK5n8B+HkAFQDebq39Z2NMDWg29vJiD0araLY+K47QJEUyMOBy8LKoKaZolZX86fVS2I8epYg+8wyPm5qiKJaVcRKR8kopqQyHeSsv5znE2166SYkhW+ExgQDPVVbGSSaRcJNKKMQdtgcPUvAlDy9RuHyeoSH81bty6JmO4Qx24RgOYACtADzu+yjM10uzkpqakm4urn+zxWVNVTTGmL0AMtbas/n7dQCi1tpzxR6o1sFvfdZUJSER+Oioq3kX90lpP1jYxSqTYRrnBz/g7cIFF42HwxTIbJapFKmyCYV4Cwb5U0zPRMgnJym6s7POEtnv52sCAb4ml+NkkM1ywbWlhamZXbsWl3kGg3jgE6P4zLt7UJ0eggc5TCOGnrJu/Oa79uO1v9vqJoUrNRcPBp3Ya3NxZRlWm4M312rNdz2vWQkq8KXBmiO0XI5COzbmhNbjce0DgcVdrCoq+PzFi8B3vgN897vM4c/N8fGaGud1Lw3KrXU5+3CYguz38768Vko/p6aYc5cdtdIVS5qUi5VyJMIP3NTk+s1WV+OBJ2vxNx+IYGFkBndWn8fdL7+E227OL9Du3s1UVHOzE/vlmotXV3PBd5vk65XrY7UC/20AnwHw+cKF1HzDjx8B8DoA37LWfqRYA1WBV55DIkGhHx93/WilKXgyuXwXq9FRfPsd38LFj3wLbfMnUOmbR2u7Bw17aymUySRz+RMTruRSFlwrKxk9F/a7le5QsoNVdtvKFYBcDfj9PK6mxlUJSTooHGYePxp15Zfy/pWVFPv9+3lFIHn4KzUXl3y9NhdXsHqBD4AVNHcD6AIwBSAAwAvgAQDvs9Y+VcyBqsAryyIVLmNjTGEAFDjxgZGUDgCEQrj/GzH8P38Qw1g8jBBm8DI8iJ8038Br9p5AU3jO5bplt+2lS4snkUCAQlxV5dYBpMG4+MiLjXIi4Y7z+Sj24rXT3MwFiKYmjjWZdLX09fV8/cgIJxtJL4mf/f79i5uNa3Nx5QqseSerMcYPoBZA3Fo7VeTxXUYFXrkukkkK3dgYNzmJWIfDFNvpabz6R+cwdAlIw48ZRDGNGGYQxd6WORz7+28CDz7INM7MjLNXqKtzte5iFwy46hrp51pXxwhfSiaHhxcfIxu0pJm5WBl3dbFmvrGR5xVLhEiE728t00z9/RyX38/jZDG3KW/gKq6f4+PaXFwpXasCZZsjXZnGxvgToFjW1sJfE0EEs4hhGjFMw4ssLAzmUYFTw5VMo0xPM1//4IP0yhGxj8UouAsLjOxlZy1A0a6ocDYEdXXOdyYepzgPDrpNWtLuUMS+upp+OXv30iAtGnV1+YGAW1QVw7aLFxmx+3wU+/37ufmqo4Pj0ebi2x4VeKX0kUYd+R6ur/ppH54ZqsEYapFEOcKYRwzT2N80hQe/WBCZSynm+DjwyCNcpO3poViK/7ukVkZGOAlI20K/n5GzRPetrfzp8/H4/n7eJG8vQu7xMMpuaGDe/aabWIFjjJtIamtdV6vxcTY4OXHC5eyrqzlJ3HorrwxCIefRv0HNxZWNYUMF3hjjBfAYgAFr7auv9loVeKUozMzg8x8aw7v+aAqJhMUcKij0wSr80wc8uPsXrtLFKhxmyuWxx4Ann+RGLHGKjOY3SiUSzlBNmpL7fC7/Lm6aeVOyp/9jEscfHEBNqg+Nngm0V04j5k+5pibBIBdWDxxgdN7WxveQ921s5AaD5maWkD75JPDss7y6kB20HR1M5XR0OHMz8dK5Ac3FV4LWwReXYuTgOwB0W2u/bowJAvBZa2ev881/H8AhsHZeBX4bsFn+gH/nTRnc/4FxVOXGEPYk8Jqf9+KP3l3Q1BtYvouV1N4PDDB6Pn2agiolm4EAo+S5Od4kOs9keHy+rHMwUYmvHm/HaXQhhXLUYgKNGMRP7O1Hixl2kb2UYEYinBxuu41iX1fnWhz6/a5BubQvfOopbvgaHOR5QiF+6Tt3MqUTCrlJSapw1qG5+PWibpLFZ60bnd4I4DCAamvtTmNMN4B/vJ6drMaYVgAfBXAvaFqmAl/ibJY/4CNHgN/8zQK9xhyafGN4z9sn8ZOvzG94qs2XTBbmqa/UxcrnY5Tf00Oh7+ujMMfjFExpQj415Uo3vV7AWjz1eBLpXA5eADOIoQftOI8d8Eci+OM35qtnLl1yXjuygUquKLq6KPY338xIPZXie4TDHH9bG9MwqRQ3fR0/znPJa6SJeVWV68QlJZ6S86+tXXNz8etls3jRbJYgpBisVeCfAnAngEettbflH3vGWnvTdbzxpwG8E7QY/h9XEnhjzGFwAkF7e/sdPVf611e2DJvlD7i21vmZFVJXncXIyQmmOkSgq6p4wFLf9qVdrLJZ3qTxd28vxVQiZMmhT00xX28t/uNJHxIIwsIggATCmIcHOcQRwgt+ro1VNbEYUylDQxR8yfVLZF9WRhHfsYN2xgcOMK0ju2plUbW+3k0C4u8zNsbXRKMubVRezs8uFg2yB6Chwa0jrFO+/mqnvVHLgZslCCkWaxX4R621zzfGPGmtvc0Y4wPwhLX25msc92oAP2mtfbMx5kexjMAXohH81mez2MFel5DMz1MAJyZcFUtdHaP6pQ09pIvV1BSFMZl0UfvFi66O3e93jUfGxvDQp0dQkR6DhUUcQYyjEln40OifxYv2TLhdsE1NLtJOJpkakmocEXtrXUlnVxej+o4O59Pj9zubhMp8pVAmQxvmU6fcjFdXx+M7O/mZx8ZctZB44zc0cF2goYH3iyT4Pp9zdS7E63XZrfVmswQhxWKtAv8ucJPTrwP4XQBvBnDcWnvPNY57J4BfA5ABN0hFAdxvrf3V5Y5Rgd/6bJY/nhVFirkcRV5KG41xUX0kcuWT5OvtL0f3MzOMvHt6+DOVAoJBHD1Vhq9+MY06O4guXEQlpuAB0LijAg0H6ijYU1O8okgmKfbV1UytSJnj4CCj+5ERTjLpNMcYDLo0TXc3j6mrc7X3kYizYojFeNzZsxT88XGeo66O1Tj791Ps5SpieNjtMaiq4gRUVeV2+67SG2czRPCbJQgpFmsVeA+ANwD4cdAe+GsAPrgSDxqN4LcPm+Xyd7kUTU0NdXxZ4nFnjZDNUixra3ngcqKWzbqFWjm2r48lkhMTOHHK4IHvhzEwG0FjxQJ++uYedOfOuAqeWIzRcijkzNbm5lwZZl0d37+8nM/39fHnwgLDXjFiq61liqWpiemahgYeF41S7MUSORqleF+44CJ7Y3jMnj28MohGOaH097t0FsCxFk4cchMf/muwGQKAzTCGYrJWgQ8DSFhrs/n7XgDlK2nZpwK/vdgMC1hHjgCvf71zLwAYHH/4w9c5llzOWSPMzrqG2rW1164pl8bgEnn39LjdqWVlzgJhepobrM6ccbnwykoKdDTK9x4b4zjEbK2ykmMIBinM+Unk8hqAbNQqzMk3NvLW3OyicI/HpXRSKY7xzBkn9g0NTuxDIWf+JtYMPh+PF18guaKQ5iliz3yFf5eNDgA2wxiKyVoF/hEAr7DWzuXvVwB4wFr7wmIPVAVeKSZFm2iWGp6Vlbnqk2uVGcrmo95e3np6GIEnEjw2FmOEPj7OaLpwk1VFBYU2GuWkMTrq8v+FKZpwmO8xNMTnpaG4VAqJCVswSNFvaWG4Kukcj8cZtqVSHOfZszyn1OHv2cMNWeXli5uL53LOShngOCXPIQZrktYJhQCvd9MEABs9hmKx5ioaa+2t13qsGKjAK5uaKxmeRaMU0crKay9E5hdecfEiI/eLFynKiQQFsrKSt4kJRtNDQ84+QSYV6fgkO1YXFii04n5ZXs4rjuFhim0269IydXU8XgS5spLqtmOHMzWTxiXhMMW+r48VQ5OTTuz37qXYyzjyzcVRVuauELJZTlTz887TB3A7f+VWok1NbiRrFfjvAvhda+0T+ft3AHivtfYFxR6oCryyZUilXApFdrJKrl6i2athLSPyixcZLYvYp1JOkEMhCvz58xRzycuLr43YGS8sMF8+O8vfxb5YzNCmphY5bV4eZ0WFi8DDYQp9V5fzphf//WDQiX1PjxP7piaK/YEDPI80K5H3qalx/vXSx1aaqEspjde7WPDD4edWMClXZa0C/zwA/wZgMP9QE4BftNY+XtRRQgW+VCily99rYi1FTQzPrL1seHbdzbQzGR5/4QJv584trqqRSp6FBdewJJFY3Hg8EnG59ZERF91LXj6bxdjQAhZGFmCRBeBDRXMENXsa3QKylGwGg4t3w4pNslxJJBLM/ff18TMbw0lh716mcqRhiby/NCsp/D4SicWiH4+7zyMTjuTzi1imWYoUyy54D1hFc9Jamy7uEIkK/Nan1BawVkQ67QzPkklGp5Krv95URDxOcZdo+dy5ywZqlxuH5HK8v7DA12cyri5frIMrKynaMzPA8DDG+hYw0J9GBoAPKVQggTKkEYt5EK0qd6WZkcjlXbjwePiP19DA0hPJ5wN83OdzYt/f7xajm5vZWH3XLo5zYsLZJIgL59Lm4rncYsEXJ07AjaMwn68tDC+z2oYfL7PWftMY89orPW+tvb+IYwSgAl8KlFoJ2qqZnXVVJ9Y6a4Hq6uuL6gutkIeH+eX19LjIXlIcIoIiylKyOVGwiaq6Gp/6YhkWEmk0YRhRTKMMafiRQgQJdNYnXQvDcJi5+sZGJ8IeD88lNsmtrU6oRXz9fk44skFLqoLEGrmjgyK/tFlJTc3yk18qtTits7DgonwZ6wrLNEuR1Qr8O6y1f2qM+ecrPG2tta8v5iABFfhSoNQ2kayZTAafvm8C//Tno5gcSqChyYM3/mE1XvNbtdfv6iiVOLLrtreXQjo66qJ4qWiRUktpSj48DAwP41vfSiMDH2ZRgXmEkIIPdZhAFabw4oNzzltH/pFCIUbzDQ1M00j6x+fjecNhvofU2ldV8Zjyct7m5xnVDw05V8zWVtojt7cz8l9pc3Fr+XkLo/xkks9dZ5lmKbLqFE1+k9MvWGs/uV6DK0QFfuujEfxiClNWYcyhFmNoDkziT+7J4VWvDTprhOs1+iq0V5iZoYAODLg1AIl0AQpcfT1QX4933xtHdL4PHehDAElkYRBHELY8hFe/NkihlEXjmRmeozAnX1Pj6vOlVaLk7aUePhJxDVAkRRQMckyyJ0BKPFtbmcJpaeFjq20unk4/N7VzjTLNUmOti6wPW2tfsi4jW4IK/NZnW+fgr8CVJjwPsrildQJPPJDfjXo1w7PlKNyINTVFURbDstFRV1UzMwP4fDgzHsFnv9eC07l2hDCPvTiDHejFLd3zaGqAq4OPRHhuSQ2NjbncvqRFamuZwgmHKeSRiIu8Cxua1Nfz84gtcTjMMQ0N0ftG8vLt7a56Rzz2V9tc3FqOV0o0t0GZ5loF/k8AxAH8O4B5edxaO1HMQQIq8KXCZqmi2QzjuGbKamHBReRSsy5ljNdbLljYzWp+nqI+N0eRHxigmI6Noe9cAsdP+9GbrMFMpAN3/WI7XnRrHDh2jLPQzAzTL14vRVWEe2KCz09MuJSI9JKVHbPh8OIG4B7P4mbkUkUTjVL0JbIXsZe2hm1tvNxrbHTWyeKHU1Ozuubi2eziXP78PL7ypSze9z5g4JIXseYw3vK2MF77a1uzTHOtAn/hCg9ba+2OYgyuEBV4pVhsliuJ605Z5XLODqDQtkCsEa6X2VmK/eQkP7w0JJmcdK6XUuUjOfSuLgprPM7mIb29PIdU7lRUcAweD68W+vr4fDrtovWKCqZmqqtd7r6x0VXdSO4ccA1HIhF+xlCI4x4Z4VWDiHpbG1M5DQ3P9bBfQ3PxI0eA331jAiY+jzB4qw7E8cf3WLzqVdhyZZrak1XZdmyWtYBVTTTxOAW00Bqhtpa36y0PzGYXTxiyIDk/z/OeP0+hnpykkFdUUJB37mSuPV4Q2UtNveTUJY0zM8OFVLEZ9npdrbzYFldXM8/e2spIX3a4Tk25UszKSlehEw7z+dFR57VfXs7jW1qY4xdf4UjE5etXkFu/0v8Ngxz2ti3g+A/mtlyZ5loj+ABoEfwjACyA74AdnRJXPXAVqMArxWIzVfOsOlVkrRPp2XyHTDE8i8WuP6pMJNyEIb1ek0lX1njxoqtjz2QonE1N3NlaV8fHz53jBxgZ4Tn8fifmyaTb7CWljLLwKrtupfyys5NfQmvr4k1i0iQ8FHJpnFjMpbDyDVQQDHJsYo0sk4QYrF1Hc/Hr/r8hZZoyQW7SMs21CvwnAcwC+Hj+oV8GUGWt/c9FHSVU4JXisVki+KIhVS6SGvH7Xa7+essBRVDHx519QSpFwZ6d5RczMOA8cCRN1NhIsQ+HOeEMDlLsJyY4WYizZC7H84hlQiq1WOitdeWMdXW8Wtizh6kYqfufmHA2yuKeGQotFnuJ/oNB55RZX+/KOK/RXHzV/zeWlmlKL15gQ8s01yrwR621t1zrsWKgAq8Ui82Sgy86hRugpqf52EoMzwSxE5D0SyJBgRY//AsXmCa5dMl5wVdXU0y7upgSGRtzi6SFLpYej2uCMjvr6vODQdcEXHrXlpdzktq1C7j1Voq918vzSZVQNuuiexFQWViemuLYpOVgYyMnD7/f5fqrqxeJbVH/b1xPmaaMeZ3KNNcq8B8BUzKP5O8/H8DrrLVvLvZAVeCVYrIZqmjWlcLqGRFXsUa4HsMzYWFhsQWwVMpMT1PAZdFVUiniGtnczHRJOs18+cgIBVdEzut1Vx7iI2+tW7SNRFyjcYn2q6oY2T/vefxHCwZd56yRETc2SZEEg5wAxOis0F5BbrIILBuyvF68+c0UdFk6OHwY+Id/KMK/iZRpFqZ2livTrKjAm38/sOZxrFXgT4A+NL35h9oBnACQA6tprtqbdSWowCvKKrCWkbL4xYuI1tZe/4YhOc/UFMVSFk5zOf4cHWWefnDQbbIq9MZvbeUVhDQ6EUEvTGpPTACXLmHs3ARS8TTS8GIM1fA3NeLmOyPuykTq4GMxivyhQ2xJGIk4uwOp85e6e9lFm8nwM8zOug5WjY0U+uZmoLwcn/92DL/9xzUYisdAe611vrqTMs3C2vxsFu/8S+DfP+2F1PIMoRkA8Nu/vTKRX6vAd1zteWvtFbJZq0MFXlHWyJUMz6qrKfYrqSGX88jCrNSzx+NMyfT1UfTFNRKgwIqQBgJ83cCAsyQoK8NDj/pw5lQa7ehFEwZRg0l4kIMvUI7avQ1M1USjPHZoyDlShkKcRG66ibe6Or6njFEMzWQcgYBbW5iddRYKjY140zsa8MR4O1IIYALVmEA15lFxY9dnEgnUh+cRyFHePcjhOA4AWHkDci2TVJTtyFLDM/GCX4k1AsDIU2rrs1nejOH9/n6mZyTqj8fdRqnmZgp+Os2yzOFh/Nu/LCADL0ZRgxTKEMUM9uAE2jCI7up8RB4KMRe/fz/PMzjICUXsE/x+nnf3buC22xjlBwJ8/9FR3grtlMvLFy2O/s0/liOOAIbQiEtoQi86sYAwJlGNgcQKFq3XyOLlEgu5mgBW1oBcBV5RtjOyoDo2RgH2eFxUf72GZ4DbjDU+7ipdjGHkPDzMaF0qYaRKx+vl+7S3A7W1ePOvjKIbZ9CIYfiQRhxBDKAFCQTwjt/oZ+19f78zKKuooNjffDPTTZImmpx0G60qK1kCc9ttFP3qauedPzLiatrz5Zt/95fzyMzNIYx5pFCOBQQxhGYka1rx/i93upLLqqp13dV6tfVwFXhFUVbEkSPAn79tHvG+MRxomsDvvDlveCZR/UrELJl06ZFUytWjz81R6EdG3OLo1BQFtrwcb/9gE85hJ6YQQTfOYg9OoRYTMLB47a9FKeahEHDiBMVeDMrEK6ejg17zdXVu5+vEhGtPKHXyBw4wldPezsdHRi6P6alH4vjs/RYZWEQwjwhmEUYcL3hpGfbcEnI9a7u6nKVxLFb0OncVeEVRisLS0kAPsmgJTuJ97xjDT79snmojhmfSQep6Kaytl+oZsTiWDVT5ssnvfHESZ0+nMY8wLqALp9GNLIA33fE0fmbPadc0pLaWOXevFzh6lA3JC6uFovnJYMcOt/NWrlKmpvhBpeFKdzdwyy30pS8rw9c/NYl//ZshRLITCCIOH9LwI4Nf+IlZHGie4bmk7aG4XnZ1sdZeLBaKQLH2aqjAK8o256piciLuNlFlsxQ32US1ki352ayrrZ/PTxpeL6P64WHmxufncf+/zuHM4zOoxgTKkEXLwSq84k3dFOCJCeDxx7lzVqyFpb49kWBkf/asuyoQm+KmJkbebW2M4mdnuVArNfrSSrGjA3/22X14aOZ2DKMOVZhGAy6hFqNoiS3gj98ad/1lp6edRUMkwnPv2cM0UH399fffXYZi1eOrwCvKNue6tudfyfAsFmM6ZCWWvcBz/XSk41S+VBIzMxRwWcCdmOAg6+qYXunu5marH/6QC6yplJt4Kis5YfT18SY59vJy5uwrKyn44l+Ty/E9e3qA4WE88v0MkijDMOpxGnvxGG7DeexCEEk8+rn8RCQmbdJcfXLSrV/kJwocOMCF4IYGXv2swp+mGHs1VOAVZZuz4nRAIuGi+kLDM/F2v15k561ExOIrL6ZnMplIDb5sliorYxXOzTczej95EnjySbfZKRxmmsbn46LryMjiRWSfj5G8lG52dTGdE4vhL946gPrZc+hEH4KYRw5eTCGGyXAHfv2vbuGO2mCQk8LoqEv5zM/zvnjuABxDZyePueUWRvbX22y9SKjAK8o2Z9XpABFe6fQErM7wDOBEIVG9CLFYEI+OMq0i/WbHx7nAOj9PMW9vp9gHAlx8PX7cpWkiEdcAfGjICbJYHEiqKL/T91uDO/HvJw9iEC2owyj24gS6cRb7G6awe0fe46a+Hjh4kJusmptdtyuxdpAxj4xwgsrlKPY7drCa5847ObEsbS6+DqjAK4qy9nSAVM6MjTnDM7FGWGnt+NJGJz6f26Va2EUqmXS59GSSk8rOncyDZ7MU+vPnncgGAhyb7HYVmwAR+HQax57NIJn1YBoxnEI3HsPzcAFd2Fs9gff915PA6dPuWLE+7u6mcB84wMcLrxgmJjixDA87b5xQiGM8dAh44Qsp9uvUPUoFXtmWlLwXzUYhrpRijQAwipb8+ErSE7mcsyiQKwSfj4It6RvZ1jk353bQ5nKuQqatjee4cIF5qEzGGZzJ5ifZ7BUI4KuPR5CFF1HMogJzMDCYRQQnsQdvfP9dPOfMDM936pTbjWsMJ5C2NhfdBwIuspe2idJsfHzcuV7u3s2o/mUvo9gX0U9eBV7ZdpSsm+RmI5126QspYZRNVCuNWFMpV+oopmIARXNqipGzMRTNsTEK6fg431MsjWtrGV339/M1Ivbx+OUmIqefXkA868EYajCMOhhYNGIEDd4p7N8DplX27AHuuos/5+d5BXH2LKOF0VGeV65g9uwB7riDi7qy0Wtykr+fP881gtFR15Fq507gR34EePnLmf5ZY75eBV7ZdpScH/xWQJp3iF+7NOiurl65iEkEPznpovFEgvdlUdbjodD29rpyEZY2UgAAEZlJREFUyECAotnaSqEeGWE0LX466TTOPjGBvkcGUItR+JBBEuXoRxt2vKQV+9vivEqYmHCmbd3ddLfs7uaEJm0LL15kWkaasciC6803czOWdNWSBWZpmjI66jZldXYCL3oR8MpXcsyryNerwCvbjs3U0WnbIYupkktfreEZ8NzSTfnHm5ujsM7PU9RzOT6WL4VEIsEJRtr8+f2XF3ifOZrBF7+YQwjzaEI/OjCAakywAKYpwo1Nu3bx9efO8WcuR7HfuRO4/XYKs8fjrgx6exmpy85ecbHcv595+2iUE+DUFCePc+eYAhoedgvFX/3qqnxwVOCVbYdG8JuEpZH4ag3PgOcu8kr6ZSa/+zSdZlScy1FsBwcpoADFuakJiMXw+3/ghZ2aQBRzALLwIosYJnCg7AJe0T3AScPr5cSwbx//0wwOMt0yMcH3jUa5sHPTTYy8xeZhfp45+4EBvvd8wS7hXbso+M3NHKs0Gr9wgb+/732rSteowCvbDs3BbzJkl6vUkHs8zhqhomJl5xL/e0kHZbMUzHSa55bdp2VljOQlqh8dBfx+vPP9FRhCI2YRgYVBFaYQwgI8yODP3pZh/v7iRaZ9ZLdsezsXVmtr+fz5827hVso4u7o4iUjnpkzGtTjs73dlnWKBIJNHIMDXv+xlq/pqrybw62eVpigbiIi4VtFsEiQirqtbXCI5Pk6Bk01U12N4Zgwj6GjUiahMHH4/J4xkkqmSXI5CuncvBbanBx6MYT9OIoFyzCKKMVRjAE0IIg1UzfP4zk5ODpI3P3+eN0nTHDrE9xocZI5fng8GGaFLk5FQyHnYS3llTw+PO3PGNUzZtw94yUuK7l6pEbyiKBtDLueiekllVFZS7KPRlZ+v0B4hleL9XI5RszQDqajAT/xoHDUYQTt6UYdxBJBACn5MI4q3/3XeTCyT4fHSIUoWSYeGePVQaGTW2cmrCHG2lJLKYNCVjkoT8MpKino2y9f19vKc1gIf+1jRUzQawSuKsjF4PBTA2lrX7Fsai6zG8CwYdP4zhfYI0oTEWiCVQmOdxcBoEy5iB2KYQSMG0YJ+dFVMAOcmnVulpI+iUZ6jtZVif+mSa0r+/e/TQqGpieWSe/dyMhkdXfyZ+vt5rljM9WStrGRkf9ttRa2LL0QFXlGUjScY5AailhZnjTAwwFSGWCNEo9dXRihXApWVzrZYUjizs/i11xu8+289CKYSSMOP09iLgbJuvPy3poAdvUyjTE7yONnJWl/PyL6mhimY7m6K+IULHGNvL1MvVVX8HDt3MvpPJBipp1JMGw0N8ZxlZUzfBAL87I2NKzOBv05U4BVF2TxIt6nqagqiRMBTU4xyJeK/XsMzae/X0HDZ4OwV1RPIls3jY/80j+ERg5aGDN74+hz+049FgeDzWPkzNUXRFkuC0VFeVYg1Q0UFRX/HDk4Evb1cmB0bA559luZozc1cRG1qotAvLLhG5FLXn0ox5SM9b4vMuuXgjTFtAP4FQCOAHID7rLXvudoxmoNXlNJnxRYS4kg5NuasESSFUlm5cmHM5SjgMnFIhF1WxvSMx8OUjjGumUl//2U/+8uVMw0NrtyzsOzx9GlnbwDwCqSjg7n6dNrZJGcyONvrwzefrELffBQfa3s77n2nZ2vYBRtjmgA0WWufMMZEADwO4DXW2uPLHaMCryilzZrLV8WfXRZS8w6RqK1dXfONVMotzEqLQWkO4vM5oU8kKO5DQ25Dk1gnVFY6T3hrmXufnmbK5uxZZ3Hs8TAF1d0N1NXh2CPT+N7X5uBDAgsI4XfwPoRCvq3Z8MMY83kA77XWPrjca1TgFaW0KdoGNDE8k6hebAXq6lbvxz476zZSTU9T0KWJSFmZ2wYtzUAGBrjgOjHByFwmm9ZWzlqZjNu9evIkP+D4OM8TCuHTx7rxeHIvPAAyKMO78DYAZuu17DPGdAJ4GMBBa+3MkucOAzgMAO3t7Xf0XOlfX1GUkmBdLCTSaSfMyaQrYVyN4Rmw2ENGNlNlMky1SGSfyzGCn5ujiF+6RMGfnOTx4TAnm44OZ2kgi8dPPQUMDeHYUwvIwoth1OExPA9/hHcC8K/4u9hQgTfGVAB4CMC91tr7r/ZajeAVpbRZdwsJ2eFauMu0tpbpk5VaIwAU8fFxplnEEri8nOeLRHjOZJLvu7DA9x0aotiLKVpVlTNAk/z71BQ++Kfn0Zk4iXqMIIUyPA+PAigvagS/rlU0xhg/gM8AOHItcVcUpfS5994r5+DvvbdIbxCJuAbZUh7Z00P3RzE8C4ev/3yBAPPmzc1uwXVoyDX5iEYZqTc0OI/6+nrWw4+Oupy9VNZIVL93L/b9RiM++YGDCGfHEMIMAH9xvwus7yKrAfBRABPW2t+7nmM0gleU0ueGN2KRXqpieCY7TGtqVhfVZzIU+JERpmakhLOqivXsPh9TMjMzrrn42JjbtZrNclZrbsZDAzvwkX8LYmYshcfbX4t7/8JsmSqaHwHwHQDPgGWSAPBH1tr/s9wxKvCKoqwbSw3PxOWxtpZR/2pYWGBUPzDASWRhgVF9UxOvGKSn7fQ0UzPSgrCnh+PwePj6ffuA171uVV40G5Kisdb+B4D17TarKIpyvSxneDYxsXLDMyEUcu6QU1OM6nt7aSQmm7Y6Opi2kf6tYjU8P8/6+p4epnBWczVxDdRsTFGU7cvShiJrNTwDXFVPXx+j9bk5llrKQqsxfM/JSXzj/ml8/CNp9I/6cab9x4ueolGrAkVRti8eD6P2mhpWzBQanpWVuaj+eq0RAObjGxt5m5+ny+TFi3SjPHuWUX1XFz759F687b1xBOPjKEMKPb0Ghw/zFMVak9AIXlEUpRDJm4+NLbYbqK3lz9V4xsiVQm8v0zIzMzj8eyEcHWvCOezEDKJIg+36tkyZpKIoypZDFl+rqhYbnp07x+hcNlGtpH9q4ZXC/v3A8DBOj51HO3qxA+cxjho8iB8D4EFvb/E+igq8oijKcpSXuzp4MTy7dIm3SMRZI6wkqi8vB9rbcbGjHY/3zKIdPYhgFgDtFdrbizd8FXhFUZRrUegxLwZlY2Ns07dKwzNu+org+MLBy48Ve6OTCryiKMpKKCtjnXtTkzM8GxnhYmpFhbNGuIbh2Y3oG6yLrIqiKGslk3FRfSLBmnaxRgiF1vWtdZFVURRlPfH5XOeouTnuah0f589QiEIvzUFu5LBu6LspiqKUOhUVvGWzLqqX8kixRqiouCFDUYFXFEVZD7xeWhTU13PDk1gjjI87w7Pq6lX5z1wvKvCKoijrTTjMW2urs0bo61sc1a/W8OwqqMAriqLcKLxeinltLc3HZBPVzAxw882r2yV7FVTgFUVRNoJgkI1JWlpcA+8is4rOtIqiKErR8HjWrZRSBV5RFKVEUYFXFEUpUVTgFUVRShQVeEVRlBJFBV5RFKVEUYFXFEUpUVTgFUVRShQVeEVRlBJFBV5RFKVEUYFXFEUpUVTgFUVRShQVeEVRlBJFBV5RlG3HkSNAZyd9vjo7eb8UUbtgRVG2FUeOAIcPAwsLvN/Tw/sAcPfdGzeu9UAjeEVRthX33OPEXVhY4OOlhgq8oijbit7elT2+lVGBVxRlW9HevrLHtzIq8IqibCvuvfe5DZRCIT5eaqjAK4qyrbj7buC++4CODrZB7ejg/VJbYAW0ikZRlG3I3XeXpqAvRSN4RVGUEkUFXlEUpURRgVcURSlRVOAVRVFKFBV4RVGUEsVYazd6DJcxxowC6Fnl4bUAxoo4nK2MfheL0e9jMfp9OErhu+iw1tZd6YlNJfBrwRjzmLX20EaPYzOg38Vi9PtYjH4fjlL/LjRFoyiKUqKowCuKopQopSTw9230ADYR+l0sRr+Pxej34Sjp76JkcvCKoijKYkopglcURVEKUIFXFEUpUba8wBtjKo0xnzbGnDTGnDDGvGCjx7SRGGPeaow5Zox51hjzCWNMYKPHdCMxxnzYGDNijHm24LFqY8yDxpgz+Z9VGznGG8Uy38Vf5f9WnjbGfNYYU7mRY7yRXOn7KHjufxhjrDGmdiPGtl5seYEH8B4AX7XW7gVwC4ATGzyeDcMY0wLgLQAOWWsPAvAC+KWNHdUN5yMAXrnksf8J4BvW2m4A38jf3w58BM/9Lh4EcNBaezOA0wDedqMHtYF8BM/9PmCMaQPwYwBKrmnflhZ4Y0wUwEsAfAgArLUpa+3Uxo5qw/EBCBpjfABCAAY3eDw3FGvtwwAmljz8swA+mv/9owBec0MHtUFc6buw1j5grc3k7z4CoPWGD2yDWOb/BgD8LYA/AFByFSdbWuAB7AAwCuCfjTFPGmM+aIwJb/SgNgpr7QCAd4ORyBCAaWvtAxs7qk1Bg7V2CADyP+s3eDybhdcD+MpGD2IjMcb8DIABa+3RjR7LerDVBd4H4HYA77fW3gZgHtvn8vs55HPLPwugC0AzgLAx5lc3dlTKZsQYcw+ADIAjGz2WjcIYEwJwD4D/b6PHsl5sdYHvB9BvrX00f//ToOBvV14B4IK1dtRamwZwP4AXbvCYNgPDxpgmAMj/HNng8WwoxpjXAXg1gLvt9t4IsxMMho4aYy6C6aonjDGNGzqqIrKlBd5aewlAnzFmT/6hlwM4voFD2mh6AdxljAkZYwz4fWzbRecCvgDgdfnfXwfg8xs4lg3FGPNKAH8I4GestQsbPZ6NxFr7jLW23lrbaa3tBAPG2/O6UhJsaYHP87sAjhhjngZwK4C/2ODxbBj5K5lPA3gCwDPgv29Jb8VeijHmEwC+D2CPMabfGPMGAH8J4MeMMWfAaom/3Mgx3iiW+S7eCyAC4EFjzFPGmH/c0EHeQJb5PkoatSpQFEUpUUohglcURVGugAq8oihKiaICryiKUqKowCuKopQoKvCKoigligq8ohRgjLnNGPPBDXrvr28Xp0vlxqACryiL+SMAf79eJ8+bwC3HxwC8eb3eW9l+qMArWxJjzOeMMY/nve8PFzz+BmPMaWPMt40xHzDGvDf/eJ0x5jPGmB/mby+6wjkjAG621h41xnjy/vF1+ec8xpizxpja5c5ljLnTGPO9vPHd92SHtTHmN4wxnzLGfBHAA8aYJmPMw/mNRs8aY16cH8IXAPzy+n5zynbiatGEomxmXm+tnTDGBAH80BjzGQDlAP4E9COaBfBNAOIS+B4Af2ut/Q9jTDuArwHYt+SchwA8CwDW2pwx5uMA7gbwv0Gfn6PW2jFjzL8uc66TAF5irc0YY14B7qr++fy5XwBOHhPGmP8O4GvW2nuNMV7Q1hnW2kljTLkxpsZaO17cr0vZjqjAK1uVtxhjfi7/exuAbgCNAB6y1k4AgDHmUwB251/zCgD7adEDAIgaYyLW2tmCczaB9tPCh0Hfmv8NWuv+89XOBSAG4KPGmG7QW9xfcK4HZVwAfgjgw8YYP4DPWWufKnjdCOgEqgKvrBkVeGXLYYz5UVBkX2CtXTDGfBtAAIC5ymGe/OvjV3lNPH8eAIC1ts8YM2yMeRmA54PR/LLnMsb8PYBvWWt/zhjTCeDbBU/PF5z3YWPMSwD8FICPGWP+ylr7L/mnA/lxKMqa0Ry8shWJAZjMi/teAHflH/8BgJcaY6ryi5k/X3DMAwB+R+4YY269wnlPANi15LEPAvg4gE9aa7PXOFcMwED+999YbvDGmA4AI9baD4DdyG7PP27Aq5CLyx2rKCtBBV7ZinwVgC/vIPpnYOs56Wj1FwAeBfB10Dp6On/MWwAcyjebPg7gTUtPaq09CSCWT7cIXwBQAZeeudq53gXgncaY74L9cJfjRwE8ZYx5EpyE3pN//A4AjxS01FOUNaFukkpJYYypsNbO5SP4zwL4sLX2sys4/q0AZq21H8zfPwQuqL746keuHWPMewB8wVr7jfV+L2V7oBG8Umq83RjzFFgNcwHA51Z4/PsBJAHAGPM/AXwGwNuKOsLleVbFXSkmGsEriqKUKBrBK4qilCgq8IqiKCWKCryiKEqJogKvKIpSoqjAK4qilCj/F4asJUDhG8mhAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(age, price, 'bo')\n",
    "plt.xlabel('age (years)'); plt.ylabel('price ($1000\\'s)')\n",
    "xvals = np.linspace(age.min(), age.max())\n",
    "for i in range(50):\n",
    "    b0,b1,tau = trace_tuned[np.random.randint(0, 1000)]\n",
    "    plt.plot(xvals, b0 + b1*xvals, 'r-', alpha=0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hamiltonian Monte Carlo\n",
    "\n",
    "While flexible and easy to implement, Metropolis-Hastings sampling is a random walk\n",
    "sampler that might not be statistically efficient for many models. Specifically, for models of high dimension, random walk jumping algorithms do not perform well. It is not enough to simply guess at the next sample location; we need to make each iteration a useful draw from the posterior whenever we can, in order to have an efficient sampler for bigger models.\n",
    "\n",
    "![from Hoffman and Gelman 2014](http://d.pr/i/RAA+)\n",
    "\n",
    "(*image: Hoffman and Gelman, 2014*)\n",
    "\n",
    "Since Bayesian inference is all about calculating expectations over posteriors, what we seek is an algorithm that samples from the area of the parameter space that contains most of the non-zero probability. This region is called the **typical set**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What's a Typical Set?\n",
    "\n",
    "The typical set is where most of the probability lies in a particular volume associated with the distribution. As the dimension of a model increases, this set moves progressively further from the mode, and becomes more singular, as the result of concentration of measure.\n",
    "\n",
    "The typical set is a product of both the density, which is highest at the mode, and volume (that we integrate over), which increasingly becomes larger away from the mode as dimensionality increases. In fact, at high dimensions, the region around the mode contributes almost nothing to the expectation. We need an algorithm that will find this narrow region and explore it efficiently.\n",
    "\n",
    "![](images/typical_set_.png)\n",
    "\n",
    "(image: Betancourt 2017)\n",
    "\n",
    "In this context, and when sampling from continuous variables, Hamiltonian (or Hybrid) Monte\n",
    "Carlo (HMC) can prove to be a powerful tool. It avoids\n",
    "random walk behavior by simulating a physical system governed by\n",
    "Hamiltonian dynamics, potentially avoiding tricky conditional\n",
    "distributions in the process."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulating Hamiltonian Dynamics\n",
    "\n",
    "In HMC, model samples are obtained by simulating a physical system,\n",
    "where particles move about a high-dimensional landscape, subject to\n",
    "potential and kinetic energies. Adapting the notation from [Neal (1993)](http://www.cs.toronto.edu/~radford/review.abstract.html),\n",
    "particles are characterized by a position vector or state\n",
    "$s \\in \\mathcal{R}^D$ and velocity vector $\\phi \\in \\mathcal{R}^D$. The\n",
    "combined state of a particle is denoted as $\\chi=(s,\\phi)$. \n",
    "\n",
    "The joint **canonical distribution** of the position and velocity can be expressed as a product of the marginal position (which is of interest) and the conditional distribution of the velocity:\n",
    "\n",
    "$$\\pi(s, \\phi) = \\pi(\\phi | s) \\pi(s)$$\n",
    "\n",
    "This joint probability can also be written in terms of an invariant **Hamiltonian function**:\n",
    "\n",
    "$$\\pi(s, \\phi) \\propto \\exp(-H(s,\\phi))$$\n",
    "\n",
    "The Hamiltonian is then defined as the sum of potential energy $E(s)$ and kinetic energy\n",
    "$K(\\phi)$, as follows:\n",
    "\n",
    "$$\\mathcal{H}(s,\\phi) = E(s) + K(\\phi)\n",
    "= E(s) + \\frac{1}{2} \\sum_i \\phi_i^2$$\n",
    "\n",
    "Instead of sampling $p(s)$ directly, HMC operates by sampling from the canonical distribution.\n",
    "\n",
    "$$p(s,\\phi) = \\frac{1}{Z} \\exp(-\\mathcal{H}(s,\\phi))=p(s)p(\\phi)$$.\n",
    "\n",
    "If we choose a momentum that is independent of position, marginalizing over $\\phi$ is\n",
    "trivial and recovers the original distribution of interest.\n",
    "\n",
    "The Hamiltonian $\\mathcal{H}$ is independent of the parameterization of the model, and therefore, captures the geometry of the phase space distribution, including typical set. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Hamiltonian Dynamics**\n",
    "\n",
    "State $s$ and velocity $\\phi$ are modified such that\n",
    "$\\mathcal{H}(s,\\phi)$ remains constant throughout the simulation. The\n",
    "differential equations are given by:\n",
    "\n",
    "$$\\begin{aligned}\\frac{ds_i}{dt} &= \\frac{\\partial \\mathcal{H}}{\\partial \\phi_i} = \\phi_i \\\\\n",
    "\\frac{d\\phi_i}{dt} &= - \\frac{\\partial \\mathcal{H}}{\\partial s_i}\n",
    "= - \\frac{\\partial E}{\\partial s_i}\n",
    "\\end{aligned}$$\n",
    "\n",
    "As shown in [Neal (1993)](http://www.cs.toronto.edu/~radford/review.abstract.html), \n",
    "the above transformation preserves volume and is\n",
    "reversible. The above dynamics can thus be used as transition operators\n",
    "of a Markov chain and will leave $p(s,\\phi)$ invariant. That chain by\n",
    "itself is not ergodic however, since simulating the dynamics maintains a\n",
    "fixed Hamiltonian $\\mathcal{H}(s,\\phi)$. HMC thus alternates Hamiltonian\n",
    "dynamic steps, with Gibbs sampling of the velocity. Because $p(s)$ and\n",
    "$p(\\phi)$ are independent, sampling $\\phi_{new} \\sim p(\\phi|s)$ is\n",
    "trivial since $p(\\phi|s)=p(\\phi)$, where $p(\\phi)$ is often taken to be\n",
    "the univariate Gaussian.\n",
    "\n",
    "![](images/skate_park.jpg)\n",
    "\n",
    "**The Leap-Frog Algorithm**\n",
    "\n",
    "In practice, we cannot simulate Hamiltonian dynamics exactly because of\n",
    "the problem of time discretization. There are several ways one can do\n",
    "this. To maintain invariance of the Markov chain however, care must be\n",
    "taken to preserve the properties of *volume conservation* and *time\n",
    "reversibility*. The **leap-frog algorithm** maintains these properties\n",
    "and operates in 3 steps:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\phi_i(t + \\epsilon/2) &= \\phi_i(t) - \\frac{\\epsilon}{2} \\frac{\\partial{}}{\\partial s_i} E(s(t)) \\\\\n",
    "s_i(t + \\epsilon) &= s_i(t) + \\epsilon \\phi_i(t + \\epsilon/2) \\\\\n",
    "\\phi_i(t + \\epsilon) &= \\phi_i(t + \\epsilon/2) - \\frac{\\epsilon}{2} \\frac{\\partial{}}{\\partial s_i} E(s(t + \\epsilon)) \n",
    "\\end{aligned}$$\n",
    "\n",
    "We thus perform a half-step update of the velocity at time\n",
    "$t+\\epsilon/2$, which is then used to compute $s(t + \\epsilon)$ and\n",
    "$\\phi(t + \\epsilon)$.\n",
    "\n",
    "**Accept / Reject**\n",
    "\n",
    "In practice, using finite stepsizes $\\epsilon$ will not preserve\n",
    "$\\mathcal{H}(s,\\phi)$ exactly and will introduce bias in the simulation.\n",
    "Also, rounding errors due to the use of floating point numbers means\n",
    "that the above transformation will not be perfectly reversible.\n",
    "\n",
    "HMC cancels these effects **exactly** by adding a Metropolis\n",
    "accept/reject stage, after $n$ leapfrog steps. The new state\n",
    "$\\chi' = (s',\\phi')$ is accepted with probability $p_{acc}(\\chi,\\chi')$,\n",
    "defined as:\n",
    "\n",
    "$$p_{acc}(\\chi,\\chi') = min \\left( 1, \\frac{\\exp(-\\mathcal{H}(s',\\phi')}{\\exp(-\\mathcal{H}(s,\\phi)} \\right)$$\n",
    "\n",
    "**HMC Algorithm**\n",
    "\n",
    "We obtain a new HMC sample as follows:\n",
    "\n",
    "1.  sample a new velocity from a univariate Gaussian distribution\n",
    "2.  perform $n$ leapfrog steps to obtain the new state $\\chi'$\n",
    "3.  perform accept/reject move of $\\chi'$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Normal mixture\n",
    "\n",
    "HMC as implemented in PyMC3 is heavily automated. To provide some innsight into how the components of HMC work, let's look at a simpler implementation provided by [`minimc`](https://github.com/ColCarroll/minimc), a package created by Colin Carroll. This can be used to illustrate leapfrog integration and the paths taken for HMC sampling.\n",
    "\n",
    "The example we will employ here is a mixture of three bivariate normal distribution, each with its own location and covariance. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7ad23c691898>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from autograd import grad\n",
    "import autograd.numpy as np\n",
    "from minimc import mixture, neg_log_mvnormal\n",
    "\n",
    "# Plotting helper function\n",
    "def neg_log_p_to_img(neg_log_p, extent=None, num=100):\n",
    "    if extent is None:\n",
    "        extent = (-3, 3, -3, 3)\n",
    "    X, Y = np.meshgrid(np.linspace(*extent[:2], num), np.linspace(*extent[2:], num))\n",
    "    Z = np.array([np.exp(-neg_log_p(j)) for j in np.array((X.ravel(), Y.ravel())).T]).reshape(X.shape)\n",
    "    return Z, extent\n",
    "\n",
    "np.random.seed(7)\n",
    "\n",
    "mu1 = np.ones(2)\n",
    "cov1 = 0.5 * np.array([[1., 0.7],\n",
    "                       [0.7, 1.]])\n",
    "mu2 = -mu1\n",
    "cov2 = 0.2 * np.array([[1., -0.6],\n",
    "                       [-0.6, 1.]])\n",
    "\n",
    "mu3 = np.array([-1., 2.])\n",
    "cov3 = 0.3 * np.eye(2)\n",
    "\n",
    "neg_log_p = mixture([neg_log_mvnormal(mu1, cov1), \n",
    "                     neg_log_mvnormal(mu2, cov2), \n",
    "                     neg_log_mvnormal(mu3, cov3)], [0.3, 0.3, 0.4])\n",
    "\n",
    "Z, extent = neg_log_p_to_img(neg_log_p, (-3, 4, -3, 4), num=200)\n",
    "\n",
    "plt.imshow(Z, alpha=0.9, extent=extent, cmap='afmhot_r', origin='top')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Though simple, this would be very challenging for a Metropolis sampler, which would have a great deal of difficulty crossing the areas of low probabilities between the peaks. Most of the time, you would end up with an estimate of one of the three components, leaving the others entirely unexplored."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Leapfrog Integration\n",
    "\n",
    "We can explore the paths taken by HMC samplers by simulating from a leapfrog integrator, which varies by the amount of momentum and the size and number of steps taken."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "from minimc.minimc_slow import leapfrog, hamiltonian_monte_carlo\n",
    "from minimc import neg_log_mvnormal\n",
    "\n",
    "dVdq = grad(neg_log_p)\n",
    "\n",
    "steps = slice(None, None, 40)\n",
    "\n",
    "positions, momentums = [], []\n",
    "for _ in range(3):\n",
    "    q, p = np.random.randn(2, 2)\n",
    "    _, _, q, p = leapfrog(q, p, dVdq, 4 * np.pi, 0.01)\n",
    "    positions.append(q)\n",
    "    momentums.append(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1512x504 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(ncols=len(positions), figsize=(7 * len(positions), 7))\n",
    "\n",
    "steps = slice(None, None, 40)\n",
    "\n",
    "Z, extent = neg_log_p_to_img(neg_log_p, (-3, 4, -3, 4), num=200)\n",
    "\n",
    "for idx, (ax, q, p) in enumerate(zip(axes.ravel(), positions, momentums)):\n",
    "    ax.imshow(Z, alpha=0.9, extent=extent, cmap='afmhot_r', origin='top')\n",
    "\n",
    "    ax.quiver(q[steps, 0], q[steps, 1], p[steps, 0], p[steps, 1], headwidth=6, \n",
    "              scale=60, headlength=7, alpha=0.8, color='C0')\n",
    "    ax.plot(q[:, 0], q[:, 1], '-', lw=3, color='C0')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hamiltonian Monte Carlo\n",
    "\n",
    "Rolling leapfrog integration into HMC requires additional choices concerning path length (how far to leapfrog)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 10/10 [00:02<00:00,  4.08it/s]\n",
      "100%|██████████| 10/10 [00:03<00:00,  2.72it/s]\n",
      "100%|██████████| 10/10 [00:06<00:00,  1.78it/s]\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(111)\n",
    "ss, pp, mm, pl = [], [], [], [1, 2, 4]\n",
    "for path_len in pl:\n",
    "    samples, positions, momentums, accepted = hamiltonian_monte_carlo(10, \n",
    "                                                                      neg_log_p, \n",
    "                                                                      np.random.randn(2), \n",
    "                                                                      path_len=path_len, \n",
    "                                                                      step_size=0.01)\n",
    "    ss.append(samples)\n",
    "    pp.append(positions)\n",
    "    mm.append(momentums)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1512x504 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(ncols=len(ss), figsize=(7 * len(ss), 7))\n",
    "\n",
    "Z, extent = neg_log_p_to_img(neg_log_p, (-3, 4, -3, 4), num=200)\n",
    "steps = slice(None, None, 20)\n",
    "\n",
    "for ax, samples, positions, momentums, path_len in zip(axes.ravel(), ss, pp, mm, pl):\n",
    "    ax.imshow(Z, alpha=0.9, extent=extent, cmap='afmhot_r', origin='top')\n",
    "\n",
    "    for q, p in zip(positions, momentums):\n",
    "        ax.quiver(q[steps, 0], q[steps, 1], p[steps, 0], p[steps, 1], headwidth=6, \n",
    "                  scale=60, headlength=7, alpha=0.8)\n",
    "        ax.plot(q[:, 0], q[:, 1], 'k-', lw=3)\n",
    "\n",
    "    ax.plot(samples[:, 0], samples[:, 1], 'o', color='w', mfc='C1', ms=10)\n",
    "    ax.set_title(f'Path length of {path_len}')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## To Learn More\n",
    "\n",
    "- **Neal, R. M. (2010)** [MCMC using Hamiltonian dynamics](http://www.mcmchandbook.net/HandbookChapter5.pdf), in the Handbook of Markov Chain Monte Carlo, S. Brooks, A. Gelman, G. L. Jones, and X.-L. Meng (editors), Chapman & Hall / CRC Press, pp. 113-162.\n",
    "- **Michael Betancourt's \"[A Conceptual Introduction to Hamiltonian Monte Carlo](https://arxiv.org/abs/1701.02434)\"** A thorough, readable reference that is the main source here\n",
    "- **Hoffman, M. D., and A. Gelman. (2014)**. “The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo.” Journal of Machine Learning Research: JMLR 15 (1): 1593–1623.\n",
    "- **[Hamiltonian Monte Carlo from Scratch](https://colindcarroll.com/2019/04/11/hamiltonian-monte-carlo-from-scratch/)**, by Colin Carroll, from which the HMC code was stolen."
   ]
  }
 ],
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